20260323 Anotações Capital e Categorias

up:: 099 MOC Anotações // 20260302 Anotações Categorias e Capital (Espaço Comum de Organizações)

Dialectics

• “Objects” need be situated (contingent). I.e. they can be changed
• Contradiction between these objects and their surroundings.
• Negation and change of the objects’ situation

Level theory

We can see the dialectical aspects better when we see this asymmetry of these aspects of the theory: “upper” levels are heterogeneous and contingent to the lower ones, but the “lower” ones are homogeneous and are related to structural restrictions as far as the upper ones are concerned.

E.g. when capital $K$ is consolidated, then labor power $l$ is understandable by its wage, i.e. it is understood at a lower level (i.e. the [stabilized] commodity space $\mathbb{C}$).

Mystification/Fetishism through level theory

Mystification: $p\to q$ at level 1, and $q\to q^{\prime }$ at level 2, then mystification happens when we can “believe” that $q$ can influence things at a level it is not.

Fetishism: Processes which happen at a new level can’t explain their coming-of-being from a lower level merely through the new-level processes.

Commodity fetishism as per Marx: “the relation of the producers to the sum total of their own labour is presented to them as a social relation, existing not between themselves, but between the products of their labour”.

That is, producers $l$ at a lower level, products $p$ at a higher level, and the production process $P:l\to p$. $P$ is “abstracted away”, and what’s left is a “relation between things” which seems to reproduce their (the producers’) own relation with themselves.

Capital levels

Lowest level is the commodity level: just commodity circulation and exchanges.

A level above would be money begets money: this amount of money $m_1$ becomes that amount of money $m_2$, that is, labor power and means of production produce commodities which have more value (and sell for more value) than spent.

A level beyond would be total social capital accumulation: this capital $K_1$ becomes that capital $K_2$.

Law of capital accumulation

The form of immiseration (misery) of the working class is a projection of the organic composition of total social capital.

The trajectory of the working class between its possible states — floating, latent, stagnant, pauperized — yields more information about the total social capital than about individual capitals.

This, in fact, is a definition of domination: the power of a totality is imposed upon a whole level/class. That is, the aggregate effect of actions of dominating individuals imposes itself upon the dominated individuals’ lives.

Bi-Heyting Algebras

Accounting for property and affinity, aside from value.

A presheaf topos for value already yields a bi-Heyting algebra for free (thm). There are now Heyting-valued functions

$$\{\begin{array}{l}e(a,b)\in \mathcal{H}\\ p(a,b)\in \mathcal{H}\\ a(a,b)\in \mathcal{H}\end{array}$$

for evaluation, property and affinity.